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In Wang et al. (2002), the mode I crack problem has been analyzed for a functionally graded material strip with arbitrarily distributed properties. For the completeness of the research, this paper provides an analysis method for the mode II in plane and mode III anti-plane elastic crack problems for a functionally graded material (FGM) strip containing a crack along the gradient direction. In the analysis, the gradient region is treated as a number of homogeneous layers stacked along the gradient direction. The analytical models developed in this paper for the modes II and III problems, together with the model developed in Wang et al. (2002) for the mode I crack problem complete the analysis of the mixed-mode crack problem for functionally graded materials with a crack parallel the gradient direction. Those analytical models allow the material properties be any continuous functions along the thickness direction of the strip. [ABSTRACT FROM AUTHOR]

In order to avoid introduction of an error when a local crack growth criterion is used in an incremental crack growth formulation, each straight crack extension would have to be infinitesimal or have its direction corrected. In this paper a new procedure to correct the crack extension direction is proposed in connection with crack growth analyzed by the Dual Boundary Element Method (DBEM). The proposed correction procedure and a reference correction procedure already described in the literature are evaluated by solving two different computational crack growth examples. In the two examples it is found that analyses of the crack paths performed with the proposed crack correction procedure using big increments of crack extension are in excellent agreement with analyses of the crack paths performed by using very small increments of crack extension. Furthermore, it is shown that the reference correction procedure has a tendency to overcorrect the crack growth direction if the stop criterion for the iterative correction procedure is not calibrated in each new crack growth analysis. [ABSTRACT FROM AUTHOR]

The present paper deals with the measurements of the critical Crack Tip Opening Angle by using an instrumented test. There is a comparison between the analysis of results made by a well known kinematic model and those given by finite element analysis based on a cohesive model for node release. Analysis is performed both on simple specimens and on back slotted ones. [ABSTRACT FROM AUTHOR]

The paper addresses special features of nonlocalized and localized fatigue damage in metals and alloys. The sizes of maximum fatigue cracks at a fatigue limit in metals and alloys of various grain sizes and strengths are analyzed. The authors discuss the linear and nonlinear fracture mechanics criteria that relate the fatigue crack sizes and the fatigue limits. The experimental values of the fatigue crack size are compared to those calculated by different criteria. Special features of initiation of nonpropagating fatigue cracks in the presence of stress concentrators are studied. [ABSTRACT FROM AUTHOR]

Abstract  Dynamic failure events such as armor penetration and explosive fragmentation are too complex to be treated by classical single-crack continuum fracture mechanics. In such cases deformation and fracture result from multiple cracks, voids, and shear bands acting simultaneously and influencing one another’s evolution. An alternative “meso” fracture mechanics is needed that treats microfailure activity while permitting fast and inexpensive predictive computations. This paper discusses the approach and experiments that elucidate and quantify failure physics on the micron level. “Rosetta Stone” experiments that isolate a damage mode, produce statistical distributions of damage features, and “freeze in” damage at various stages of development are described and illustrated. The observations and data lead to equations describing nucleation and growth of cracks, voids, and shear bands. The resulting mesomechanical material failure models link the microworld with the macroworld and can be used in continuum hydrocodes for fast, efficient simulations of dynamic fracture scenarios. [ABSTRACT FROM AUTHOR]

A general numerical tool for the analysis of three–dimensional bimaterial interface cracks is presented in this paper. The proposed tool is based on a multidomain formulation of the Boundary Element Method (BEM), with the crack located at the interface of the domain. Mixed mode stress intensity factors are computed along the three-dimensional crack fronts using the Energy Domain Integral (EDI) methodology and decoupled via the Interaction Integral. The capability of the procedure is demonstrated by solving a number of examples. The last of these examples consists in a thick centre cracked panel for which the behaviour of the J-integral and the mixed-mode stress intensity factors along the crack front is studied as a function of the material mismatch. [ABSTRACT FROM AUTHOR]

Weld bead geometry cannot, by its nature, be precisely defined. Parameters such as bead shape and toe radius vary from joint to joint even in well-controlled manufacturing operations. In the present paper the weld toe region is modelled as a sharp, zero radius, V-shaped notch and the intensity of asymptotic stress distributions obeying Williams’ solution are quantified by means of the Notch Stress Intensity Factors (NSIFs). When the constancy of the angle included between weld flanks and main plates is assured and the angle is large enough to make mode II contribution non-singular, mode I NSIF can be directly used to summarise the fatigue strength of welded joints having very different geometry. By using a large amount of experimental data taken from the literature and related to a V-notch angle of 135°, two NSIF-based bands are reported for steel and aluminium welded joints under a nominal load ratio about equal to zero. A third band is reported for steel welded joints with failures originated from the weld roots, where the lack of penetration zone is treated as a crack-like notch and units for NSIFs are the same as conventional SIF used in LEFM. Afterwards, in order to overcome the problem related to the variability of the V-notch opening angle, the synthesis is made by simply using a scalar quantity, i.e. the mean value of the strain energy averaged in the structural volume surrounding the notch tips. This energy is given in closed form on the basis of the relevant NSIFs for modes I and II and the radius RC of the averaging zone is carefully identified with reference to conventional arc welding processes. RC for welded joints made of steel and aluminium considered here is 0.28 mm and 0.12 mm, respectively. Different values of RC might characterise welded joints obtained from high-power processes, in particular from automated laser beam welding. The local-energy based criterion is applied to steel welded joints under prevailing mode I (with failures both at the weld root and toe) and to aluminium welded joints under mode I and mixed load modes (with mode II contribution prevailing on that ascribable to mode I). Surprising, the mean value of ΔW related to the two groups of welded materials was found practically coincident at 2 million cycles. More than 750 fatigue data have been considered in the analyses reported herein. [ABSTRACT FROM AUTHOR]

The paper reports on the results from analysis of some nonclassical fracture problems that allow for stresses along cracks. The results have been obtained by the author and his collaborators at the Institute of Mechanics (Kiev) since 1980 [ABSTRACT FROM AUTHOR]

The simple extension tear test-piece also referred to as the trousers sample is widely used to study crack propagation in rubber. The corresponding energy release rate, called tearing energy for rubber materials, was first established by Rivlin and Thomas ( J Polym Sci, 10:291–318, 1953); a second derivation was proposed later by Eshelby (In G.C. Sih, H. C. van Elst, and D. Broek, editors, Prospects of Fracture Mechanics, 69-84, Leyden, 1975). We show here that the derivation of this result can be advantageously revisited through the scope of Configurational Mechanics. Our approach is based on the rigorous definition of the configurations of the body and on the physical significance of the configurational stress tensor. More precisely, it is demonstrated that the change in energy due to crack growth, and then the tearing energy, is directly related to the components of the configurational stress tensor in the body. [ABSTRACT FROM AUTHOR]

The sectional thickness of plate-like components has a significant influence on the fatigue and fracture properties. This effect is primarily due to the differences in the through-the-thickness stresses prevailing at the tip of a crack in a finite-thickness plate or shell. Characterization of this effect to date has remained largely empirical. The current paper presents new analytical results for CTOD for the through-the-thickness crack in infinite plates with various thicknesses. These results are based on a recently developed solution for an edge dislocation in infinite plate of arbitrary thickness. The analytical predictions of the CTOD and the constraint factor are compared with the three-dimensional FE results. It is shown that the analytical and the numerical results are in good agreement when the numerical calculations are not affected by the size of the FE mesh and by the boundaries of the FE model. [ABSTRACT FROM AUTHOR]

Mechanical behavior of ceramics and glass under local loading of specimens by an indentor is studied experimentally by a proposed test procedure. The effect of scratching on fracture resistance is assessed by comparing the test results obtained by two methods - edge fracture under scratching (S+EF method) and without scratching (EF method). Based on the analysis of experimental findings, the fracture mechanism of these brittle materials under such test conditions is discussed. [ABSTRACT FROM AUTHOR]

This research is concerned with the fracture mechanics of a laminated composite medium, which contains a central layer sandwiched by two outer layers. There is a periodic array of cracks in the central layer along the central axis of the medium. Fourier transform is used to reduce the problem to the solution of a system of dual integral equations, which are solved by the singular integral equation technique. Rigorous fracture mechanics analysis, which exactly satisfies all boundary conditions of the problem, is conducted. Numerical solutions for the crack tip field and the stress in the medium are obtained for various values such as crack length, crack spacing and layer thickness. Results are also given for the reduction of the equivalent Young’s modulus of the laminate due to multiple cracking. The cases of axial extension and residual temperature change of the composite medium are accounted for. [ABSTRACT FROM AUTHOR]

We will solve a fracture-mechanics problem for an elastic material with cracks subject to a polyharmonic load created by longitudinal waves with different wavelengths propagating through the material. The frictionless contact between the edges of a finite-length plane crack under the action of two normal harmonic tension/compression waves with different frequencies is studied. The forces of contact interaction and displacement discontinuity are analyzed. The effect of the wave frequency on the stress intensity factor is examined for different normalized wave numbers. [ABSTRACT FROM AUTHOR]

The fracture mechanics concepts were applied to describe the experimental results of three-points bending tests to investigate fracture characteristics and crack resistance of unfired earth material. [ABSTRACT FROM AUTHOR]

The continuous growth of 3D cracks under cyclic loading conditions is considered within a discrete simulation procedure. It is performed within the framework of linear elastic fracture mechanics. An incremental procedure is applied to consider the non-linear behavior of crack growth within the simulation. In each increment the direction and magnitude of the crack propagation for each point along the crack front are needed to define the new crack front. Within the present context the crack deflection results from the maximum tangential stress criterion and the crack extension is obtained by the evaluation of a crack propagation rate. To simulate the crack propagation as exactly as possible the evolution of the stress field between two consecutive crack fronts is taken into account. The analysis of the changing stress field is utilized for optimization of the predicted crack fronts. The whole procedure is realized in terms of a predictor–corrector scheme. Numerical examples are presented to demonstrate the benefits of this concept. [ABSTRACT FROM AUTHOR]

For defects in solids, when displaced within the material, reciprocity relations have been established recently similar to the theorems attributed to Betti and Maxwell. These theorems are applied to crack- and defect-interaction problems. [ABSTRACT FROM AUTHOR]

The article examines the laws governing deformation changes of the fresh-ice structure, which depend on the loading conditions. Visualization of the defect-accumulation scenario was gained for the fracture made as a result of pressing a plane stamp of a circular cross section into the ice. The correlation of the scale factor with the size of an ice structural element is demonstrated. The fracture toughness, as well as the fracture work and the energy spent to produce a crack, is calculated.

The tear resistance of polyethylene terephthalate film is characterized by the essential work of fracture method in mode I as a function of test speed and temperature. Attempts to extrapolate tearing resistance found by the method of essential work to commercial slitting processes are discussed. Limitations of the essential work of fracture method with regards to specimen size are evaluated. Based on the findings modifications to the test protocol are suggested. [ABSTRACT FROM AUTHOR]

An extension of the Neuber-Novozhilov structural fracture propagation criterion is presented for mode I (tensile) and mode II (shear) propagation under compressive loads. In addition to allowing numerical simulation of crack growth, the criterion can be used to model change of propagation mode, crack branching, and coalescence. The criterion can be applied effectively when the SIF is calculated accurately (at least three significant digits). A numerical method is suggested for this purpose that consists of complementing the complex variable hypersingular boundary element method (CVH-BEM) with special procedures for automatically tracing crack propagation and coalescence. The CVH-BEM code with the structural criterion has been used to investigate crack propagation in compression for both small and non-small fracture process zone (FPZ). The results of numerical experiments are in agreement with the analytical conclusions available for the case of small FPZ that indicates the possibility of three distinct patterns of crack propagation under external compressive loads. These are: (i) smooth curvilinear tensile (wing) cracks, (ii) stair-step propagation pattern with changing modes, and (iii) in plane shear propagation. The numerical study also indicates that when the critical size of the FPZ is large enough, the non-singular terms in the expansion of the stress functions strongly influence the crack trajectories. Specifically, this occurs when the size of the FPZ approaches a quarter of the half-length of the initial crack. Calculations for a closed initial crack in a half-space under compression illustrate the general features of crack propagation. Although the dominant direction of crack growth is that of the applied compressive stress, the pattern of propagation strongly depends on the particular geometry, critical size of the FPZ, and the ratio of shear-to-tensile microscopic strength. [ABSTRACT FROM AUTHOR]

A two-level fracture model of composites with cracks under compression is proposed. Fiber-reinforced laminated panels with a hole are considered. The panels are compressed along the fibers so that two cracks propagate from the hole boundary at a right angle to the loading direction. The fracture mechanism is analyzed at two levels. The first level is the compression-induced stress concentration at the tip of a finite-thickness crack filled with a fractured material. At this level, the theory of elasticity of linear orthotropic body is used. The second level is compression fracture at the crack tip. The analysis performed at this level involves the three-dimensional linearized theory of stability of solids, considering microcracks in the interface between the fractured and intact materials, and the exact solution describing the compression-induced instability of the cracked interface. The second level is where results obtained by the author are used. Thus, the approach proposed employs the theory of elasticity of linear orthotropic body and the three-dimensional linearized theory of stability of solids to analyze a specific mechanism of fracture [ABSTRACT FROM AUTHOR]

The cohesive zone parameters (separation energy and cohesive strength) and the crack tip triaxialities are compared between a compact tension (CT) and a double edge notched tension (DENT) specimen with smooth side-surfaces. The material is a pressure vessel steel 20MnMoNi55. The cohesive zone parameters are determined by fitting the simulated crack extensions near the midsection to the experimental data. The purpose of the study is to understand the relationship between the cohesive zone parameters and the crack tip stress triaxiality. The results show that for the same cohesive zone parameters the crack tip triaxiality near the midsection is lower in DENT specimens than in CT specimens. When the separation energy is set constant for CT and DENT specimens, the cohesive strength for the DENT specimens should be significantly lower than that for the CT specimens in order to make the simulated crack extensions near the midsection fit to the experimental data. Near the midsection, the cohesive strength and crack tip triaxiality influence each other: the specimen with a higher stress triaxiality has a higher cohesive strength; an increase of cohesive strength results in an increase of the crack tip triaxiality. [ABSTRACT FROM AUTHOR]

The structural theory of short-term damage is generalized to the case where the undamaged components of anN-component laminar composite deform nonlinearly. The basis for this generalization is the stochastic elasticity equations for anN-component laminar composite with porous components whose skeleton deforms nonlinearly. Microvolumes of the composite components meet the Huber-Mises failure criterion. Damaged microvolume balance equations are derived for the physically nonlinear materials of the composite components. Together with the equations relating macrostresses and macrostrains of the laminar composite with porous nonlinear components, they constitute a closed-form system. This system describes the coupled processes of physically nonlinear deformation and microdamage. For a two-component laminar composite, algorithms for calculating the microdamage-macrostrain relationship and plotting deformation curves are proposed. Uniaxial tension curves are plotted for the case where microdamages occur in the linearly hardening component and do not in the linearly elastic component [ABSTRACT FROM AUTHOR]

Experiments on the dynamic fracture of solids, liquids, conductors and insulators that is caused by fast intense actions of environment or directed energy fluxes reveal a number of effects indicating a fundamental difference between the fast dynamic rupture (breakdown) of materials and a similar process under slow quasistatic actions. This article analyzes examples illustrating typical dynamic effects inherent in the these processes. The article's author has proposed a unified interpretation for the fracture of solids and liquids and electrical breakdown in insulators using the structural-time approach based on the concept of the fracture incubation time.

The non–Euclidean continuum model for the description of the stress–field distribution around underground workings with a round cross section is considered. From the physical viewpoint, the non–Euclideanness parameter determines the incompatibility of elastic deformations in a rock. It is shown that disintegration zones can be identified with the parts of the rock in which this parameter takes on the maximum values and the force discontinuity criterion for the medium holds. An analysis allows one to relate the macroscopic characteristics of zonal rock fracture around a working to the non–Euclideanness parameter. [ABSTRACT FROM AUTHOR]